Заглавие | VANISHING OF THE FIRST DOLBEAULT COHOMOLOGY GROUP OF HOLOMORPHIC LINE BUNDLES ON COMPLETE INTERSECTIONS IN INFINITE DIMENSIONAL PROJECTIVE SPACE |
Вид публикация | Journal Article |
Година на публикуване | 2005 |
Автори | Kotzev B |
Списание | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Том | 97 |
ключови думи | Dolbeault cohomology groups, infinite-dimensional complex manifolds, projective manifolds, vanishing theorems |
Резюме | We consider a complex submanifold $X$ of finite codimension in an infinite-dimensional complex projective space $P$ and prove that the first Dolbeault cohomology group of all line bundles $\mathcal{O}_X(n)$, $n \in \mathbb{Z}$, vanishes when $X$ is a complete intersection and $P$ admits smooth partitions of unity. |
2000 MSC | main 32L20, secondary 58B99 |
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